How this instrument works
A frequency distribution groups raw data into a small number of equal-width class intervals and counts how many values fall into each one, turning a long, hard-to-scan list of numbers into a compact table anyone can read at a glance. It's the same idea behind a histogram's bars, expressed as a table of class boundaries and counts rather than a chart — and it's usually the first step taken before drawing a histogram at all, since the bars are built directly from this table.
The class width is calculated from the data's own range: width = (maximum − minimum) / number of classes. Each class then spans one width's worth of values, starting at the minimum, with the final class including the maximum value itself so no data point is left out — the standard convention used in introductory statistics. Every value falls into exactly one class, and the counts across all classes always add up to the total number of values entered.
This calculator produces the same underlying binning as this site's histogram and frequency-polygon instruments — all three group data the same way — but frequency-distribution reports the result as an interval table (class boundaries and counts), which is the form you'd copy directly into a written report or a textbook-style grouped-data table.
- Enter your raw numbers into Data set — any order, separated by commas, spaces or new lines.
- Set Number of classes to how many groups you want the range split into (5 to 10 is typical for most data sets).
- Read Class width to see how wide each interval is, calculated automatically from your data's range.
- Read Frequency table (class: count) for the full breakdown — each interval alongside how many values landed inside it.
- Need bars instead of a table, or points at each class's midpoint? This site's histogram and frequency-polygon instruments use this exact same binning.
Worked example — ten students' quiz scores, 5 classes
Ten students score 1 through 10 on a quiz, one student per score. Enter 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 into Data set and set Number of classes to 5. Class width = (10−1)/5 = 1.8, so the five class boundaries are 1.00, 2.80, 4.60, 6.40, 8.20, and 10.00.
Frequency table (class: count) reads '1.00 to 2.80: 2 | 2.80 to 4.60: 2 | 4.60 to 6.40: 2 | 6.40 to 8.20: 2 | 8.20 to 10.00: 2' — each 1.8-wide class happens to catch exactly two of the ten consecutive scores, a clean symmetric result that's easy to verify by hand: scores 1 and 2 fall in the first class, 3 and 4 in the second, and so on up through 9 and 10 in the last.
Questions
How is a frequency distribution different from a histogram or frequency polygon on this site?
All three group your data into the exact same equal-width classes using the same underlying calculation — they differ only in how the result is presented. Frequency-distribution shows the result as a plain interval table (class boundaries and counts), which is what you'd write into a report. Histogram frames the same counts as bar heights for a bar chart. Frequency-polygon reports the counts against each class's midpoint instead of its edges, which is what you plot to draw the connecting-line version of the same distribution. Pick whichever framing matches the output you need.
How many classes should I choose?
There's no single correct number — 5 to 10 classes is a commonly used rule of thumb for readability, balancing enough detail to show the data's shape against few enough classes that the table stays easy to read. Too few classes hides structure in the data (everything blurs into one or two bars); too many classes can leave many classes with a count of zero or one, which is just as hard to interpret.
Why does the last class include the maximum value?
Every class except the last is half-open — it includes its lower bound but not its upper bound — which would otherwise leave the single largest value in the data set with no class to belong to, since it sits exactly on the boundary of what would be an (n+1)th class. Including the maximum in the final class instead is the standard grouped-frequency-table convention, and it guarantees every value you entered is counted in exactly one class.
Can I use frequency distributions on any kind of numeric data?
Yes, for any numeric data set with at least two distinct values — test scores, measurements, ages, transaction amounts. It works less well on data that's already naturally categorical (like colors or yes/no responses) or on data where every value is identical, since there's no range to split into classes in that second case.
Do the counts across all classes always add up to my total data count?
Yes — because every class is defined so that each entered value falls into exactly one of them, with no gaps and no overlaps, the counts across all classes sum to exactly the number of values you entered. If you're checking the table by hand and the counts don't add up, it's worth re-checking which class boundary a borderline value belongs to.